Problem $3[30$ points$].$ The bar has a cross$-$sectional area $A,$ length $L,$ modulus of elasticity $E,$ and coefficient of thermal expansion $.$ The temperature of the bar changes uniformly along its length from $T_A$ at A to $T_B$ at B so that at any point $x$ along the bar $T=T_A+x\frac{T_B-T_A}{L}.$

Initially no axial force is in the bar, and the bar has a temperature $T_A.$

a$)[5$ points$]$ Determine the strain in the bar as function of $x.$

b$)$ points